Current Progress on Minimization Gem
In the first half of the summer, I plan to introduce some new numerical minimization methods to SciRuby’s Minimization gem. As per my proposal, I began by implementing the Powell’s multidimensional minimization method. Powell’s method has a better convergence in most cases than the Nelder–Mead algorithm, and is also a multidimensional minimization method which doesn’t use any derivative of the function.
I started by studying SciPy and Apache Commons library’s Powell’s optimizer. I decided to base my implementation on the method from the Apache Commons Mathematics Library. Powell’s method requires a line minimum searching algorithm, for which I used Brent minimizer (already available in SciRuby).
Having finished with Powell’s method, I am now working on the Fletcher–Reeves minimization method — a gradient method which uses the first derivative of the integrating function.